Keywords: reinforced concrete, smeared cracking, rotating cracks, compression-softening, tension-stiffening, finite element analysis.

A smeared crack model based on the rotating crack approach has been used to study the post cracking behaviour of reinforced concrete structures. A finite element program developed by the authors has been utilised to evaluate the accuracy of some of the well-known formulations proposed for the tension stiffening and compression softening phenomena. Numerical tests have been conducted and the analytical results compared with those obtained from experiments.

A 20-noded isoparametric brick element with standard serendipity shape functions has been used for the concrete. The reinforcing bars have been simulated by axial members embedded within the concrete elements, perfect bond between concrete and steel has been assumed.

The material model is based on a rotating crack approach and includes various compression softening and tension stiffening models. The reinforcement was modelled as a uniaxial elastic, linear work-hardening material.

An elasto-plastic work hardening model followed by a perfectly plastic plateau is used for the compressive regime. The crushing of concrete is considered to be a strain controlled phenomenon, defined by a function similar to the yield surface.

A rotating crack model based on total strain, which evaluates the stress strain relationship in the direction of the principal strain, was chosen

Three tension stiffening models, a simple linear model, the CEB-FIP bilinear model [1] and a non-linear model suggested by Hordijk [2] were used to represent the normal stress-normal strain relationship of concrete after cracking. The compression softening effect was modelled using the rules proposed by Vecchio and Collins [3], Cervenka [4] and Belarbi and Hsu [5].

Two numerical tests including an anisotropically reinforced panel subjected to in-plane shear loading and a beam under combined bending and torsional loads were numerically tested and the results were compared with experiments.

At the early stages of cracking the compression softening phenomenon has insignificant effects, however, as the failure load is approached, a considerable improvement in the analytical results was obtained by considering the compression softening effects. It is shown that the Vecchio and Collins [3] model gives the best predictions of the behaviour for the models tested in this study compared to the experimental results. Inclusion of the tension-stiffening effects can improve the accuracy of the numerical results compared to the experimental results. The results obtained with CEB-FIP [2] model gave the best fit to the experimental results, the linear model showed a slightly stiffer response, especially in the early stages of cracking and the Hordijk model resulted in a softer response.

1

Hordijk D.A. "Local approach to Fatigue of Concrete", PhD Thesis, University of Delft, The Netherlands, 1991.

2

Comite Euro-International Du Beton "CEB-FIP Model Code 1990", Thomas Telford, London, 1993.

3

Vecchio F.J. and Collins M.P. "The modified compression-Field Theory for Reinforced Concrete Elements Subjected to Shear", ACI Structural Journal, Vol. 83, 218-231, 1986.

4

Cervenka V. "A Constitutive Model for Cracked Reinforced Concrete", ACI Journal, Vol. 82, 877-882, 1985.

5

Belarbi A. and Hsu T.T.C. "Constitutive Laws of Reinforced concrete in Biaxial Tension-Compression", Research Report UHCEE 91-2, University of Houston, Houston, Texas, 1991.

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